Dependent Hierarchical Beta Process for Image Interpolation and Denoising

Mingyuan Zhou, Hongxia Yang, Guillermo Sapiro, David Dunson, Lawrence Carin
Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, PMLR 15:883-891, 2011.

Abstract

A dependent hierarchical beta process (dHBP) is developed as a prior for data that may be represented in terms of a sparse set of latent features, with covariate-dependent feature usage. The dHBP is applicable to general covariates and data models, imposing that signals with similar covariates are likely to be manifested in terms of similar features. Coupling the dHBP with the Bernoulli process, and upon marginalizing out the dHBP, the model may be interpreted as a covariate-dependent hierarchical Indian buffet process. As applications, we consider interpolation and denoising of an image, with covariates defined by the location of image patches within an image. Two types of noise models are considered: (i) typical white Gaussian noise; and (ii) spiky noise of arbitrary amplitude, distributed uniformly at random. In these examples, the features correspond to the atoms of a dictionary, learned based upon the data under test (without a priori training data). State-of-the-art performance is demonstrated, with efficient inference using hybrid Gibbs, Metropolis-Hastings and slice sampling.

Cite this Paper

BibTeX
@InProceedings{pmlr-v15-zhou11a, title = {Dependent Hierarchical Beta Process for Image Interpolation and Denoising}, author = {Zhou, Mingyuan and Yang, Hongxia and Sapiro, Guillermo and Dunson, David and Carin, Lawrence}, booktitle = {Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics}, pages = {883--891}, year = {2011}, editor = {Gordon, Geoffrey and Dunson, David and Dudík, Miroslav}, volume = {15}, series = {Proceedings of Machine Learning Research}, address = {Fort Lauderdale, FL, USA}, month = {11--13 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v15/zhou11a/zhou11a.pdf}, url = {https://proceedings.mlr.press/v15/zhou11a.html}, abstract = {A dependent hierarchical beta process (dHBP) is developed as a prior for data that may be represented in terms of a sparse set of latent features, with covariate-dependent feature usage. The dHBP is applicable to general covariates and data models, imposing that signals with similar covariates are likely to be manifested in terms of similar features. Coupling the dHBP with the Bernoulli process, and upon marginalizing out the dHBP, the model may be interpreted as a covariate-dependent hierarchical Indian buffet process. As applications, we consider interpolation and denoising of an image, with covariates defined by the location of image patches within an image. Two types of noise models are considered: (i) typical white Gaussian noise; and (ii) spiky noise of arbitrary amplitude, distributed uniformly at random. In these examples, the features correspond to the atoms of a dictionary, learned based upon the data under test (without a priori training data). State-of-the-art performance is demonstrated, with efficient inference using hybrid Gibbs, Metropolis-Hastings and slice sampling.} }
Endnote
%0 Conference Paper %T Dependent Hierarchical Beta Process for Image Interpolation and Denoising %A Mingyuan Zhou %A Hongxia Yang %A Guillermo Sapiro %A David Dunson %A Lawrence Carin %B Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2011 %E Geoffrey Gordon %E David Dunson %E Miroslav Dudík %F pmlr-v15-zhou11a %I PMLR %P 883--891 %U https://proceedings.mlr.press/v15/zhou11a.html %V 15 %X A dependent hierarchical beta process (dHBP) is developed as a prior for data that may be represented in terms of a sparse set of latent features, with covariate-dependent feature usage. The dHBP is applicable to general covariates and data models, imposing that signals with similar covariates are likely to be manifested in terms of similar features. Coupling the dHBP with the Bernoulli process, and upon marginalizing out the dHBP, the model may be interpreted as a covariate-dependent hierarchical Indian buffet process. As applications, we consider interpolation and denoising of an image, with covariates defined by the location of image patches within an image. Two types of noise models are considered: (i) typical white Gaussian noise; and (ii) spiky noise of arbitrary amplitude, distributed uniformly at random. In these examples, the features correspond to the atoms of a dictionary, learned based upon the data under test (without a priori training data). State-of-the-art performance is demonstrated, with efficient inference using hybrid Gibbs, Metropolis-Hastings and slice sampling.
RIS
TY - CPAPER TI - Dependent Hierarchical Beta Process for Image Interpolation and Denoising AU - Mingyuan Zhou AU - Hongxia Yang AU - Guillermo Sapiro AU - David Dunson AU - Lawrence Carin BT - Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics DA - 2011/06/14 ED - Geoffrey Gordon ED - David Dunson ED - Miroslav Dudík ID - pmlr-v15-zhou11a PB - PMLR DP - Proceedings of Machine Learning Research VL - 15 SP - 883 EP - 891 L1 - http://proceedings.mlr.press/v15/zhou11a/zhou11a.pdf UR - https://proceedings.mlr.press/v15/zhou11a.html AB - A dependent hierarchical beta process (dHBP) is developed as a prior for data that may be represented in terms of a sparse set of latent features, with covariate-dependent feature usage. The dHBP is applicable to general covariates and data models, imposing that signals with similar covariates are likely to be manifested in terms of similar features. Coupling the dHBP with the Bernoulli process, and upon marginalizing out the dHBP, the model may be interpreted as a covariate-dependent hierarchical Indian buffet process. As applications, we consider interpolation and denoising of an image, with covariates defined by the location of image patches within an image. Two types of noise models are considered: (i) typical white Gaussian noise; and (ii) spiky noise of arbitrary amplitude, distributed uniformly at random. In these examples, the features correspond to the atoms of a dictionary, learned based upon the data under test (without a priori training data). State-of-the-art performance is demonstrated, with efficient inference using hybrid Gibbs, Metropolis-Hastings and slice sampling. ER -
APA
Zhou, M., Yang, H., Sapiro, G., Dunson, D. & Carin, L.. (2011). Dependent Hierarchical Beta Process for Image Interpolation and Denoising. Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 15:883-891 Available from https://proceedings.mlr.press/v15/zhou11a.html.

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